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Of the last $18$ trains to pull into Castroville Station, $12$ were full. Considering this data, how many of the next $12$ trains would you expect to be full? $\newline$ $\newline$ ____ trains $\newline$

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Full solution

Q. Of the last

18

trains to pull into Castroville Station,

12

were full. Considering this data, how many of the next

12

trains would you expect to be full?

\newline

\newline

____ trains

\newline

Calculate Total Full Trains: Step $1$ : Calculate the total number of trains that were full out of the last $18$ trains. $\newline$ $12$ trains were full out of $18$ .
Determine Probability of Full Train: Step $2$ : Determine the probability that a train is full. Probability $P$ of a train being full $=$ Number of full trains $/$ Total number of trains $=$ $\frac{12}{18}$ $=$ $\frac{2}{3}$ .
Calculate Expected Full Trains: Step $3$ : Calculate the expected number of full trains among the next $12$ trains. $\newline$ Expected number of full trains $= \text{Probability of a train being full} \times \text{Number of upcoming trains} = \left(\frac{\(2\)}{\(3\)}\right) \times \(12\) = \(8\).

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